12. SOLUTIONS. Solutions to Exercises

Transcription

1 1. SOLUTIONS Solutions to Exercises Note on significant figures: If the final answer to a solution needs to be rounded off, it is given first with one nonsignificant figure, and the last significant figure is underlined. The final answer is then rounded to the correct number of significant figures. In multiple-step problems, intermediate answers are given with at least one nonsignificant figure; however, only the final answer has been rounded off. 1.1 An example of a solid solution prepared from a liquid and a solid is a dental filling made of liquid mercury and solid silver. 1. The C 4 H 9 OH molecules will be more soluble in water because their -OH ends can form hydrogen bonds with water. 1.3 The Na + ion has a larger energy of hydration because its ionic radius is smaller, giving Na + a more concentrated electric field than K Write Henry's law (S k H P) for 159 mmhg (P ), and divide it by Henry's law for one atm, or 760 mmhg (P 1 ). Then, substitute the experimental values of P 1, P, and S 1 to solve for S. S S1 khs khp1 P P1 (continued)

2 410 CHAPTER 1 Solving for S gives S PS1 P1 (159 mmhg)( g O/L) 760 mmhg 8.45 x x 10-3 g O /L 1.5 The mass of HCl in 0. percent HCl (0.0 fraction of HCl) is 0.0 x 35.0 g g HCl The mass of H O in 0. percent HCl is 35.0 g solution g HCl g H O 1.6 Calculate the moles of toluene using its molar mass of 9.14 g/mol: 35.6 g toluene x 1 mol toluene 9.14 g toluene mol toluene To calculate molality, divide the moles of toluene by the mass in kg of the solvent (C 6 H 6 ): Molality x mol toluene 0.15 kg solvent m toluene 1.7 The number of moles of toluene (previous exercise); the number of moles of benzene is 15 g benzene x 1 mol benzene g benzene mol benzene The total number of moles is , and the mole fractions are Mol fraction benzene x mol benzene mol Mol fraction toluene x mol toluene mol The sum of the mole fractions

3 SOLUTIONS This solution contains 0.10 moles of methanol dissolved in 1.00 kg of ethanol. The number of moles in 1.00 kg of ethanol is 1.00 x 10 3 g C H 5 OH x 1 mol C H OH g C H OH mol C H 5 OH The total number of moles is , and the mole fractions are Mol fraction C H 5 OH mol CH5OH 1.86 mol Mol fraction CH 3 OH 0.10 mol CH3OH 1.86 mol The sum of the mole fractions is One mole of solution contains 0.50 moles methanol and moles ethanol. The mass of this amount of ethanol, the solvent, is mol C H 5 OH x g CH5OH 1 mol C H OH g C H 5 OH ( kg) 5 The molality of methanol in the ethanol solvent is 0.50 mol CH kg C 3 H OH 5 OH m CH 3 OH 1.10 Assume an amount of solution contains one kilogram of water. The mass of urea in this mass is 3.4 mol urea x g urea 1 mol urea 05.4 g urea The total mass of solution is g g. The volume and molarity are Volume of solution g x 1 ml g ml L Molarity 3.4 mol urea L solution.9649 mol/l.96 M

4 41 CHAPTER Assume a volume equal to L of solution. Then Mass of solution 1.09 g/ml x (1.000 x 10 3 ml) 109 g Mass of urea.00 mol urea x g urea 1 mol urea 10.1 g urea Mass of water ( ) g g water ( kg) Molality.00 mol urea kg solvent m urea 1.1 Calculate the moles of naphthalene and moles of chloroform: g C 10 H 8 x 1 mol C10H g C H mol C 10H g CHCl 3 x 1 mol CHCl g CHCl mol CHCl 3 The total number of moles is mol, and the mole fraction of chloroform is Mol fraction CHCl mol CHCl mol Mol fraction C 10 H mol C mol 10 H The vapor-pressure lowering is P P X (156 mmhg)( ) mmhg C10H8 Use Raoult's law to calculate the vapor-pressure of chloroform: P P X (156 mmhg)(0.991) mmhg CHCl Solve for c m in the freezing-point-depression equation ( T K f c m ; K f in Table 1.3): C m T K f C C/m m (continued)

5 Use the molal concentration to solve for the mass of ethylene glycol: SOLUTIONS m glycol 1 kg solvent x kg solvent mol glycol mol glycol x 6.1 g glyco l 1 mol glycol x x 10-1 g glycol 1.14 Calculate the moles of ascorbic acid (vit. C) from the molality, and then divide the mass of g by the number of moles to obtain the molar mass: mol vit. C 1 kg HO g vit. C mol vit. C x kg H O mol vit C g/mol The molecular weight of ascorbic acid, or vitamin C, is 176 amu The molal concentration of white phosphorus is c m T K b C.40 C/m m The number of moles of white phosphorus (P x ) present in this solution is mol Px 1 kg CS x kg CS mol P x The molar mass of white phosphorus equals the mass divided by moles: 0.05 g mol g/mol Thus, the molecular weight of P x is 14 amu. The number of P atoms in the molecule of white phosphorus is obtained by dividing the molecular weight by the atomic weight of P: amu Px amu P Hence, the molecular formula is P 4 (x 4).

6 414 CHAPTER The number of moles of sucrose is 5.0 g sucrose x 1 mol sucrose 34.3 g sucrose mol sucrose The molarity of the solution is mol sucrose L M sucrose The osmotic pressure, π, is equal to MRT and is calculated as follows: mol sucrose 1 L x L atm K mol x 93 K atm 1.17 The number of ions from each formula unit is i. Here, i The boiling-point elevation is T b K b c m 3 x 0.51 C m x m C The boiling point of aqueous MgCl is C AlCl 3 would be most effective in coagulating colloidal sulfur because of the greater magnitude of charge on the Al ion (+3). Answers to Concept Checks 1.1 In each case, the component present in the greatest amount is the solvent. a. Mo is the solute, and Cr is the solvent. b. MgCl is the solute, and water is the solvent. c. N and O are the solutes, and Ar is the solvent.

7 SOLUTIONS The two main factors to consider when trying to determine the solubility of an ionic compound in water are ionic size and lattice energy. In this case, the lattice energy for the two compounds is the same; you can discount its effects. Since a smaller cation will have a more concentrated electric field leading to a larger energy of hydration, you would expect AB to have a greater energy of hydration; AB is the more soluble compound. 1.3 As the altitude increases, the percentage of oxygen in air decreases, and thus the partial pressure decreases. Above 3500 m, the partial pressure of oxygen in air has decreased to the point that not enough will dissolve in the water to sustain the fish. 1.4 In order to boil at a lower temperature than water, the vapor pressure of the solution (water + liquid) must be greater than that of water. To make this solution, you must add a liquid that is both soluble in water and chemically similar to water. It must have a higher vapor pressure than water and a boiling point lower than 100 C. One possible liquid is ethanol, with a boiling point of 78.3 C (Table 1.3). 1.5 By the principle of osmosis, in a brine solution, water will flow out of the pickle (lower concentration of ions) into the brine (higher concentration of ions). If the pickles were stored in a water solution, the water (lower concentration of ions) would flow into the pickle (higher concentration of ions) and cause it to swell up and probably burst. 1.6 Each of these solutions is a water solution of identical volume (normal boiling point 100 C) containing a different number of moles of solute. The boiling point of a solution can be determined by the formula T b ik b m. The solution with the largest T b will have the highest boiling point. Since K b is a constant, this will be the compound with the largest factor of i m. Also, since the volume is constant, the factor reduces to i moles. Ideally, all of the compounds will dissolve completely, so NaCl and KBr have i, and Na SO 4 and MgCl have i 3. This gives For NaCl, i moles x For Na SO 4, i moles 3 x For MgCl, i moles 3 x For KBr, i moles x The result is given from highest boiling point to lowest boiling point: MgCl > KBr > Na SO 4 > NaCl

8 416 CHAPTER Iron(III) hydroxide is a hydrophobic colloid. As the colloid forms in water, an excess of iron(iii) ion (Fe 3+ ) is present on the surface, giving each crystal an excess positive charge. These positively charged crystals repel one another, so aggregation to larger particles of iron(iii) hydroxide is prevented. When the electrodes are dipped into the colloidal solution, iron(iii) hydroxide precipitates because electrons from the negative electrode neutralize the excess positive charge on the iron(iii) hydroxide, allowing larger particles to form (precipitate). Answers to Review Questions 1.1 An example of a gaseous solution is air, in which nitrogen (78 percent) acts as a solvent for a gas such as oxygen (1 percent). Recall that the solvent is the component present in greater amount. An example of a liquid solution containing a gas is any carbonated beverage in which water acts as the solvent for carbon dioxide gas. Ethanol in water is an example of a liquid-liquid solution. An example of a solid solution is any gold-silver alloy. 1. The two factors that explain differences in solubilities are (1) the natural tendency of substances to mix together, or the natural tendency of substances to become disordered, and () the relative forces of attraction between solute species (or solvent species) compared to that between the solute and solvent species. The strongest interactions are always achieved. 1.3 This is not a case of "like dissolves like." There are strong hydrogen-bonding forces between the water molecules. For the octane to mix with water, hydrogen bonds must be broken and replaced by the much weaker London forces between water and octane. Thus, octane does not dissolve in water because the maximum forces of attraction among molecules are obtained if it does not dissolve. 1.4 In most cases, the wide differences in solubility can be explained in terms of the different energies of attraction between ions in the crystal and between ions and water. Hydration energy is used to measure the attraction of ions for water molecules, and lattice energy is used to measure the attraction of positive ions for negative ions in the crystal lattice. An ionic substance is soluble when the hydration energy is much larger than the lattice energy. An ionic substance is insoluble when the lattice energy is much larger than the hydration energy. 1.5 A sodium chloride crystal dissolves in water because of two factors. The positive Na + ion is strongly attracted to the oxygen (negative end of the water dipole) and dissolves as Na + (aq). The negative Cl - ion is strongly attracted to the hydrogens (positive end of the water dipole) and dissolves as Cl - (aq).

9 SOLUTIONS When the temperature (energy of a solution) is increased, the solubility of an ionic compound usually increases. A number of salts are exceptions to this rule, particularly a number of calcium salts such as calcium acetate, calcium sulfate, and calcium hydroxide (although the solubilities of calcium bromide, calcium chloride, calcium fluoride, and calcium iodide all increase with temperature). 1.7 Calcium chloride is an example of a salt that releases heat when it dissolves (exothermic heat of solution). Ammonium nitrate is an example of a salt that absorbs heat when it dissolves (endothermic heat of solution). 1.8 As the temperature of the solution is increased by heating, the concentration of the dissolved gas would decrease. 1.9 A carbonated beverage must be stored in a closed container because carbonated beverages must contain more carbon dioxide than is soluble in water at atmospheric pressure. It is possible to add carbon dioxide under pressure to a closed container before it is sealed and increase the solubility of carbon dioxide. This is an illustration of Le Chatelier's principle, which states that the equilibrium between gaseous and dissolved carbon dioxide is shifted in favor of the dissolved carbon dioxide by an increase in pressure According to Le Chatelier's principle, a gas is more soluble in a liquid at higher pressures because, when the gas dissolves in the liquid, the system decreases in volume, tending to decrease the applied pressure. However, when a solid dissolves in a liquid, there is very little volume change. Thus, pressure has very little effect on the solubility of a solid in a liquid The four ways to express the concentration of a solute in a solution are (1) molarity, which is moles per liter; () mass percentage of solute, which is the percentage by mass of solute contained in a given mass of solution; (3) molality, which is the moles of solute per kilogram of solvent; and (4) mole fraction, which is the moles of the component substance divided by the total moles of solution. 1.1 The vapor pressure of the solvent of the dilute solution is larger than the vapor pressure of the solvent of the more concentrated solution (Raoult s law). Thus, the more dilute solution loses solvent and becomes more concentrated while the solvent molecules in the vapor state condense into the concentrated solution making it more dilute. After sufficient time has passed, the vapor pressure of the solvent in the closed container will reach a steady value (equilibrium), at which time the concentration of solute in the two solutions will be the same In fractional distillation, the vapor that first appears over a solution will have a greater mole fraction of the more volatile component. If a portion of this is vaporized and condensed, the liquid will be still richer in the more volatile component. After successive distillation stages, eventually the more volatile component will be obtained in pure form (Figure 1.19).

10 418 CHAPTER The boiling point of the solution is higher because the nonvolatile solute lowers the vapor pressure of the solvent. Thus, the temperature must be increased to a value greater than the boiling point of the pure solvent to achieve a vapor pressure equal to atmospheric pressure One application is the use of ethylene glycol in automobile radiators as antifreeze; the glycol-water mixture usually has a freezing point well below the average low temperature during the winter. A second application is spreading sodium chloride on icy roads in the winter to melt the ice. The ice usually melts because, at equilibrium, a concentrated solution of NaCl usually freezes at a temperature below that of the roads If a pressure greater than the osmotic pressure of the ocean water is applied, the natural osmotic flow can be reversed. Then, the water solvent flows from the ocean water through a membrane to a more dilute solution or to pure water, leaving behind the salt and other ionic compounds from the ocean in a more concentrated solution Part of the light from the sun is scattered in the direction of an observer by fine particles in the clouds (Tyndall effect) rather than being completely absorbed by the clouds. The scattered light becomes visible against the darker background of dense clouds The examples are: fog is an aerosol, whipped cream is a foam, mayonnaise is an emulsion, solid silver chloride dispersed in water is a sol, and fruit jelly is a gel The polar -OH group on glycerol allows it to interact (hydrogen bond) with the polar water molecules, which means it is like water and, therefore, will dissolve in water. Benzene is a nonpolar molecule, which indicates that it is not like water and, therefore, will not dissolve in water. 1.0 Soap removes oil from a fabric by absorbing the oil into the hydrophobic centers of the soap micelles and off the surface of the fabric. Rinsing removes the micelles from contact with the fabric and leaves only water on the fabric, which can then be dried. Answers to Conceptual Problems 1.1 The amount of oxygen dissolved in water decreases as the temperature increases. Thus, at the lower temperatures, there is enough oxygen dissolved in the water to support both bass and trout. But, as the temperature rises above 3 C, there is not enough dissolved oxygen in the warm water to support the trout, who need more O than bass.

11 SOLUTIONS The salt that would best accomplish the task would be the salt that lowers the freezing point of water the most. This, in turn, will be the salt with the largest i factor. Ideally, if each salt dissolved completely, KCl, MgSO 4, and AgCl would have i. Similarly, CaCl and PbS would have i 3. Of the latter two salts, CaCl is more soluble than PbS, so its i factor is closer to three. Therefore, the salt with the largest i factor is CaCl, so it would lower the freezing point of water the most and would best accomplish the task. 1.3 The two main factors to consider when trying to determine the solubility of an ionic compound in water are ionic size and lattice energy. Ionic size is inversely related to the energy of hydration; the smaller the ion, the greater the energy of hydration. Keep in mind that the greater the energy of hydration, the more likely it is for a compound to dissolve. The amount of lattice energy is directly related to the solubility of the compound; the lower the lattice energy, the more likely it is for the compound to dissolve. Taking into account these factors, in order to increase the solubility of a compound you need to decrease the ionic size and decrease the lattice energy. Since the energy of hydration of the Y + ion is greater than that of the X + ion (making XZ less soluble), in order for XZ to be more soluble than YZ, the lattice energy must be less for the XZ compound. 1.4 a. According to Raoult's law, the addition of a nonvolatile nonelectrolyte to a solvent will lower the vapor pressure of the solvent, so we would expect the vapor pressure of such a solution to be lower than that of the pure solvent (water in this case). When a volatile solute is added to a solvent, the vapor pressure of the solution is dependent upon the mole fraction of the solute and solvent and the vapor pressures of both the solute and solvent. Since the solute is volatile (a high vapor pressure relative to water), the solution must have a higher vapor pressure than pure water. b. Keeping in mind that a solution will boil when the vapor pressure equals the pressure pushing on the surface of the solution, the solution with the greater vapor pressure will boil at a lower temperature. In this case, it is the solution with the volatile solute. 1.5 Smoke particles carry a small net charge that prevents them from forming larger particles that would settle to the bottom of the smokestack. The charged smoke particles are neutralized by the current, which then allows them to aggregate into large particles. These large particles are too big to be carried out of the stack. 1.6 a. Since beaker B contains more solute particles, according to Raoult's law, it will boil at a higher temperature than beaker A. b. More particles in solution lead to lower vapor pressure, which in turn lowers the freezing point of a solution. Since beaker B contains more solute particles, it will freeze at a lower temperature than beaker A.

12 40 CHAPTER 1 c. When separated by a semipermeable membrane, the solvent from the less concentrated solution flows into the more concentrated solution. Because of this, the water will flow from beaker A to beaker B causing an increase in the concentration of NaCl in beaker A. 1.7 Vinegar is a solution of acetic acid (solute) and water (solvent). Because the salt concentration outside the lettuce leaf is higher than inside, water will pass out of the lettuce leaf into the dressing via osmosis. The result is that the lettuce will wilt. 1.8 As a solution freezes, pure solvent forms without any of the solute present. This means that, as ocean water freezes to make icebergs, it freezes as pure water without the salt present. 1.9 To answer these questions it is necessary to determine the relative concentrations of solute particles in each beaker. With equal moles and equal volumes, the solution concentration will be directly proportional to the van t Hoff factor, i, for that compound. Urea, a nonelectrolyte, has i 1. NaCl, which is ionic, has i, and CaCl, which is also ionic, has i 3. a. The highest boiling point will correspond to the largest boiling point elevation, T b. Since T b ik b m, the largest T b will correspond to the highest value of i. Thus, the solution with CaCl (i 3) will have the highest boiling point. b. The highest freezing point will correspond to the smallest freezing point depression, T f. Since T f ik f m, the smallest T f will correspond to the smallest value of i. Thus, the solution with urea (i 1) will have the highest freezing point To answer these questions, it is necessary to determine the relative concentrations of solute particles in each beaker. In order to compare volumes, use the lines on the sides of the beakers. Beaker A has a concentration of five atoms per two volume units, 5/ or.5/1. Beaker B has a concentration of ten atoms per two volume units, 10/ or 5/1. Beaker C has a concentration of five atoms per volume unit, 5/1. Comparing the concentrations, beaker B beaker C x beaker A. a. Since P A X A P A, the solution with the highest vapor pressure is the solution with the highest mole fraction of solvent, or conversely, the lowest concentration of solute particles. Thus, the solution in beaker A will have the highest vapor pressure. b. The lowest boiling point will correspond to the smallest boiling point increase, T b. Since T b K b m, the smallest T b will correspond to the smallest concentration of solute particles (molality here). Thus, the solution in beaker A will have the lowest boiling point.

13 SOLUTIONS 41 c. For each solution to have the same freezing point, they all need the same concentration of solute particles. This can be accomplished by doubling the volume in beakers B and C. Solutions to Practice Problems Note on significant figures: If the final answer to a solution needs to be rounded off, it is given first with one nonsignificant figure, and the last significant figure is underlined. The final answer is then rounded to the correct number of significant figures. In multiple-step problems, intermediate answers are given with at least one nonsignificant figure; however, only the final answer has been rounded off. Atomic weights are rounded to two decimal places, except for that of hydrogen An example of a liquid solution prepared by dissolving a gas in a liquid is household ammonia, which consists of ammonia (NH 3 ) gas dissolved in water. 1.3 An example of a solid solution prepared from two solids is almost any alloy, such as 18-kt gold, which consists of 5 percent silver dissolved in 75 percent gold Boric acid would be more soluble in ethanol because this acid is polar and is more soluble in a more polar solvent. It can also hydrogen-bond to ethanol but not to benzene Naphthalene is more soluble in benzene because nonpolar naphthalene must break the strong hydrogen bonds between ethanol molecules and replace them with weaker London forces The order of increasing solubility is H O < CH OHCH OH < C 10 H. The solubility in nonpolar hexane increases with the decreasing polarity of the solute Acetic acid is more soluble because it is polar like ethanol and can form hydrogen bonds to it The Al 3+ ion has both a greater charge and a smaller ionic radius than Mg +, so Al 3+ should have a greater energy of hydration The F - ion has a smaller radius than the Cl - ion, so F - should have a greater hydration energy.

14 4 CHAPTER The order is Ba(IO 3 ) < Sr(IO 3 ) < Ca(IO 3 ) < Mg(IO 3 ). The iodate ion is fairly large, so the lattice energy for all these iodates should change to a smaller degree than the hydration energy of the cations. Therefore, solubility should increase with decreasing cation radius Fluorides (smaller anion): As the cation radius increases, the lattice energy of the fluoride salts decreases to a greater degree than the cation hydration energy decreases. Permanganates (larger anion): As the cation radius increases, the lattice energy of the permanganate salts decreases to a smaller degree than the cation hydration energy decreases. Therefore, the solubility of the fluorides increases with increasing cation radius, whereas the solubility of the permanganates decreases with increasing cation radius Using Henry's law, let S 1 the solubility at 1.00 atm (P 1 ), and S the solubility at 5.50 atm (P ). S PS1 P1 (5.50 atm)(0.161 g /100 ml) 1.00 atm g/100 ml 1.4 The partial pressure of N in air at 4.79 atm is 4.79 atm x atm Substituting this for P in S S 1 x P /P 1 (Henry's law), you obtain S ( g/100 ml) x atm 1.00 atm g/100 ml 1.43 First, calculate the mass of KI in the solution; then calculate the mass of water needed. Mass KI 7.5 g x 5.00 g KI 100 g solution g KI Mass H O 7.5 g soln g KI g H O Dissolve 3.63 g KI in 68.9 g of water.

15 SOLUTIONS First, calculate the mass of Na SO 4 in the solution; then calculate the mass of water needed. Mass of Na SO g solution x 6.50 g NaSO4 100 g solution 9.57 g Na SO 4 Mass of water 455 g soln g Na SO g water Dissolve 9.57 g Na SO 4 in g of water Multiply the mass of KI by 100 g of solution per 5.00 g KI (reciprocal of percentage) g KI x 100 g solution 5.00 g KI g solution 1.46 Multiply the mass of sodium sulfate by 100 g of solution per 6.50 g Na SO 4 (reciprocal of percentage) g Na SO 4 x 100 g solution 6.50 g Na SO g solution 1.47 Convert mass of vanillin (C 8 H 8 O 3, molar mass g/mol) to moles, convert mg of ether to kg, and divide for molality g vanillin x 1 mol vanillin g vanillin.570 x 10-4 mol vanillin mg ether x 1 kg/10 6 mg x 10-6 kg ether Molality x 10 mol vanillin x 10 kg ether m vanillin 1.48 Convert mass of lauryl alcohol (LA, C 1 H 5 OH, molar mass g/mol) to moles, convert g of ethanol to kg, and divide g LA x 1 mol LA g LA x 10- mol LA 165 g ethanol x 1 kg/10 3 g 165 x 10-3 kg ethanol Molality x 10 mol LA 165 x 10 kg ethanol m LA

16 44 CHAPTER Convert mass of fructose (C 6 H 1 O 6, molar mass g/mol) to moles, and then multiply by one kg H O per 0.15 mol fructose (the reciprocal of molality) g fructose x 1 mol fructose g fructose x 1kg HO 0.15 mol fructose kg (77.7 g H O) 1.50 Multiply the kg of CHCl 3 by the molality to get moles of caffeine; then convert moles to mass kg CHCl 3 x mol caffeine 1 kg CHCl 3 x 194. g caffeine 1 mol caffeine g caffeine 1.51 Convert masses to moles, and then calculate the mole fractions g alc. x 1 mol alc g alc mol alc. 1 mol H 35.0 g H O x O 18.0 g H O mol H O Mol fraction alc. mol alc. total mol mol mol Mol fraction H O mol HO total mol 1.94 mol mol Convert masses to moles, and then calculate the mole fractions..50 x 10 3 g glycol x 1 mol glycol 6.07 g glycol mol glycol.00 x mol H g H O x O 18.0 g H O mol H O Total moles mol Mol fraction H O mol HO total mol mol mol Mol fraction glycerol mol glycerol total mol mol mol

17 SOLUTIONS In the solution, for every mol of NaClO there is 1.00 kg, or 1.00 x 10 3 g, H O, so 1.00 x mol H g H O x O 18.0 g H O mol H O Total mol mol H O mol NaClO mol Mol fraction NaClO mol NaClO total mol mol mol In the solution, for every mol of H O, there is 1.00 kg, or 1.00 x 10 3 g, of H O, so 1.00 x mol H g H O x O 18.0 g H O mol H O Total mol mol H O mol H O mol Mol fraction H O mol HO mol solution mol mol The total moles of solution 3.31 mol H O mol HCl 4.31 mol. Mol fraction HCl 1 mol HC l 4.31 mol g H 3.31 mol H O x O 1 mol H O x 1 kg HO 3 10 g H O x 10 - kg H O Molality 1.00 mol HCl x 10 kg HO m 1.56 The total moles of solution 1.00 mol NH mol H O 3.44 mol. Mol fraction NH 3 1 mol NH mol g H.44 mol H O x O 1 mol H O x 1kg HO 3 10 g H O x 10 - kg H O Molality 1.00 mol NH x 10 kg HO.74.7 m

18 46 CHAPTER The mass of L of solution is 1.0 kg. In the solution, there are moles of H C O 4 (OA) for every kg of water. Convert this number of moles to mass mol OA x g OA 1 mol OA x 1 kg OA 3 10 g OA 0.05 kg OA The total mass of the solution containing kg H O and moles of OA is calculated as follows: Mass kg H O kg OA 1.05 kg Use this to relate the mass of L (1.0 kg) of solution to the amount of solute: 1.0 kg solution x mol OA 1.05 kg solution mol OA Molarity mol OA 1.00 L solution M 1.58 In the solution, there is mole of citric acid (CA) for every kg of water. Convert this number of moles to mass mol CA x 19.1 g CA 1 mol CA x 1 kg 1000 g kg CA The total mass of solution containing kg H O and moles of CA is: Mass kg H O kg CA kg g Now, use the density of the solution (1.049 g/ml) to convert this mass to liters of solution. Volume g x 1 ml g x 1 L 1000 ml L Since there are moles of CA in this volume, you can now calculate the molarity of the solution. Molarity mol CA Volume mol L M

19 SOLUTIONS In L of vinegar, there is mole of acetic acid. The total mass of the L solution is kg. Start by calculating the mass of acetic acid (AA) in the solution mol AA x g AA 1 mol AA 45.8 g AA ( kg AA) The mass of water may be found by difference: Mass H O kg soln kg AA kg H O Molality mol AA kg H O m AA 1.60 In L of beverage, there is 0.65 mole of tartaric acid. The total mass of the L beverage is kg. Start by calculating the mass of tartaric acid (TA) in the beverage mol TA x 150.1g TA 1mol TA g TA ( kg TA) The mass of water may be found by difference: Mass H O kg soln kg TA kg H O Molality 0.65 mol TA kg H O m TA 1.61 To find the mole fraction of sucrose, first find the amounts of both sucrose (suc.) and water: 0. g sucrose x 1 mol sucrose g sucrose mol sucrose 1 mol H 70.1 g H O x O 18.0 g H O mol H O X sucrose mol sucrose ( ) mol From Raoult's law, the vapor pressure (P) and lowering ( P) are o o P P X HO P ( ) (4. mmhg)( ) HO HO 1 - X suc mmhg o P P X (4. mmhg)( ) mmhg HO suc.

20 48 CHAPTER To find the mole fraction of benzene, first find the amounts of both benzene (ben.) and naphthalene (nap.): 1.0 g nap. x 5.6 g ben. x 1 mol nap. 18. g nap. 1 mol ben g ben mol nap mol ben. X nap mol nap. ( ) mol From Raoult's law, the vapor pressure (P) and lowering ( P) are o P P ben. (1 - X nap. ) (86.0 mmhg)( ) mmhg o P P ben. X nap. (86.0 mmhg)(0.0777) mmhg 1.63 Find the molality of glycerol (gly.) in the solution first: g gly. x 1 mol gly g gly mol gly. Molality mol gly kg solvent m Substitute K b 0.51 C/m and K f C/m (Table 1.3) into equations for T b and T f : T b K b m 0.51 C/m x m C T b C T f K f m C/m x m C T f C

21 SOLUTIONS Find the molality of the solution first: g S 8 x 1 mol S g S mol S 8 Molality mol S kg solvent m Substitute K b 3.08 C/m and K f 3.59 C/m (Table 1.3) into equations for T b and T f : T b K b m 3.08 C m S8 x m S C T b C C C T f K f m 3.59 C m S8 x` m S C T f C C C 1.65 Calculate T f, the freezing-point depression, and, using K f C/m (Table 1.3), the molality, c m. T f C - ( C) C c m T f K f C C/m 4.68 x x 10 - m 1.66 Calculate T f, the freezing-point depression, and, using K f C/m (Table 1.3), the molality, c m. T f C - ( C) C c m T f K f C C/m m (continued)

22 430 CHAPTER 1 Now, find the amount of urea in the solution from the definition of molality: Mol urea c m x (kg H O) mol urea 1 kg HO x kg H O mol mol urea x g urea 1 mol urea g urea 1.67 Find the moles of unknown solute from the definition of molality: Mol solute m x kg solvent mol 1 kg solvent x kg solvent x 10-4 mol Molar mass g x 10 mol g/mol The molecular weight is 1 amu Find the moles of the solute from the definition of molality: Mol solute m x kg solvent mol 1 kg solvent x kg solvent x 10-4 mol Molar mass g x 10 mol g/mol The molecular weight is 14 amu.

23 SOLUTIONS Calculate T f, the freezing-point depression, and, using K f C/m (Table 1.3), the molality, c m. T f 6.84 C C 1.14 C c m T f K f 1.14 C 8.00 C/m m Find the moles of solute by rearranging the definition of molality: Mol m x kg solvent mol 1 kg solvent x 103 x 10-6 kg solvent x 10-5 mol Molar mass x 10 g x 10 mol g/mol The molecular weight is 163 amu Calculate T f, the freezing-point depression, and, using K f C/m (Table 1.3), the molality, c m. T f C C C c m T f K f C C/m m Find the moles of solute by rearranging the definition of molality: Mol m x kg solvent mol 1 kg solvent x kg solvent mol Molar mass.500 g mol 0..0 x 10 g/mol The molecular weight is.0 x 10 amu.

24 43 CHAPTER Use the equation for osmotic pressure (π) to solve for the molarity of the solution. π M RT 1 atm 1.47 mmhg x 760 mmhg (0.081 L atm/k mol)(1 + 73)K x 10-5 mol/l Now, find the number of moles in 106 ml (0.106 L) using the molarity L x x 10 mol 1 L x 10-6 mol Molar mass 0.58 g x 10 mol x x 10 4 g/mol The molecular weight is 6.85 x 10 4 amu. 1.7 Use the equation for osmotic pressure (π) to solve for the molarity of the solution. π M RT 1 atm 3.70 mmhg x 760 mmhg (0.081 L atm/k mol)(5 + 73)K x 10-4 mol/l Now, find the number of moles in ml ( L) using the molarity L x x 10 mol 1 L x 10-5 mol Molar mass g x 10 mol x x 10 3 g/mol The molecular weight is 1.09 x 10 3 amu Begin by noting that i 3. Then, calculate T f from the product of ik f c m : 3 x o C m x m C The freezing point C C C.

25 1.74 Start by noting that i 4. Then, calculate T f from the product of ik f c m : SOLUTIONS x C m x m C The freezing point C C C Begin by calculating the molarity of Cr(NH 3 ) 5 Cl x 10 - g Cr(NH 3 ) 5 Cl 3 x 1 mol Cr(NH 3) 5Cl g Cr(NH 3) 5Cl x 10-5 mol Cr(NH 3 ) 5 Cl 3 Molarity x 10 mol Cr(NH 3) 5Cl L M Now find the hypothetical osmotic pressure, assuming Cr(NH 3 ) 5 Cl 3 does not ionize: π MRT (.30 x 10-3 M) x L atm K mol x 98 K x 760 mmhg 1 atm 4.77 mmhg The measured osmotic pressure is greater than the hypothetical osmotic pressure. The number of ions formed per formula unit equals the ratio of the measured pressure to the hypothetical pressure: i 119 mmhg 4.77 mmhg.78 3 ions/formula unit 1.76 Begin by calculating the molality of the solution after rearranging T b K b c m : c m Tb Kb 5 C 0.51 C/m 9.76 m The 9.76 m is the molality of the ions, not of the NaCl. The molality of the NaCl will be 9.76 m 4.88 m because i. Thus, 4.88 moles of NaCl must be dissolved in the one kg of water. This is converted to mass using the molar mass of NaCl: 4.88 mol NaCl x 58.5 g NaCl 1 mol NaCl 85 3 x 10 g NaCl

26 434 CHAPTER a. Aerosol (liquid water in air) b. Sol [solid Mg(OH) in liquid water] c. Foam (air in liquid soap solution) d. Sol (solid silt in liquid water) 1.78 a. Aerosol (liquid water in air) b. Foam (air in liquid egg white) c. Aerosol (solid dust particles in air) d. Emulsion (liquid oil in liquid vinegar) 1.79 Because the As S 3 particles are negatively charged, the effective coagulation requires a highly charged cation, so Al (SO 4 ) 3 is the best choice The K 3 PO 4 contains highly charged PO 4 3- ions that will be strongly attracted to the positively charged solution and will cause it to coagulate. Solutions to General Problems 1.81 Using Henry's law [S S 1 x (P /P 1 ), where P atm], find the solubility of each gas at P, its partial pressure. For N, P x 1.00 atm atm; for O, P 0.00 atm. P N : S x P 1 P O : S x P 1 ( g/l H O) x ( g/l H O) x atm 1.00 atm g/l H O 0.00 atm 1.00 atm g/l H O In 1.00 L of the water, there are g of N and g of O. If the water is heated to drive off both dissolved gases, the gas mixture that is expelled will contain g of N and g of O. (continued)

27 SOLUTIONS 435 Convert both masses to moles using the molar masses: 1 mol N g N x 8.01 g N x 10-4 mol 1 mol O g O x 3.00 g O.456 x 10-4 mol Now calculate the mole fractions of each gas: X N mol N total mol x 10 mol -4 ( ) x 10 mol X O 1 - X N 1.8 Using Henry's law [S S 1 x (P /P 1 ), where P atm], find the solubility of each gas at P, its partial pressure. For CH 4, P x 1.00 atm atm; for C H 6, P x 1.00 atm atm. P atm CH4 : S x (0.03 g/ L HO ) x g/ L HO P atm P atm C H6 : S x (0.059 g/ L HO ) x g/ L HO P atm When 1.00 L of the water saturated with the gas mixture is heated, g of CH 4 and g of C H 6 will be expelled. Convert these to moles using molar masses: 1 mol CH g CH 4 x g CH x 10-3 mol g C H 6 x 1 mol CH g CH x 10-4 mol Now, find the mole fractions of each gas: XCH 4 mol CH4 total mol x 10 mol -3 ( ) x 10 mol XC 1- X H6 CH

28 436 CHAPTER Assume a volume of L whose mass is then 1.04 kg. Use the percent composition given to find the mass of each of the components of the solution kg NH 1.04 kg soln x 4Cl kg soln kg NH 4Cl Mass of H O 1.04 kg soln kg NH 4 Cl kg H O Convert mass of NH 4 Cl and water to moles: 1 mol NH g NH 4 Cl x 4Cl g NH Cl mol NH 4 Cl 1 mol H g H O x O g H O 5.01 mol H O Molarity mol NH4Cl L solution 1.67 mol 1.00 L M mol NH Molality 4Cl kg H O 1.67 mol kg HO m X NH 4 Cl mol NH4Cl total moles 1.67 mol ( ) mol Assume a volume of L whose mass is then 1.17 kg. Use the percent composition given to find the mass of each of the components of the solution kg soln x 7.0 kg LiCl kg soln kg 304. g LiCl Mass of H O 1.17 kg soln kg LiCl 0.87 kg 8.7 g H O Convert mass of LiCl and water to moles: 304. g LiCl x 1 mol LiCl 4.39 g LiC l mol LiCl 1 mol H 8.7 g H O x O g H O mol H O Total moles mol (continued)

29 SOLUTIONS 437 The various quantities can now be calculated. Molarity mol LiCl L soln mol LiC l L soln M Molality mol LiCl kg HO mol LiCl 0.87 kg HO m X LiCl mol LiCl total moles mol LiC l mol In 1.00 mol of gas mixture, there are 0.51 mol of propane (pro.) and 0.49 mol of butane (but.). First, calculate the masses of these components mol pro. x g pro. 1 mol pro..491 g pro mol but. x 58.1 g but. 1 mol but g but. The mass of 1.00 mol of gas mixture is the sum of the masses of the two components:.491 g pro g but g mixture Therefore, in g of the mixture, there are.491 g of propane and g of butane. For a sample with a mass of 55 g: 55 g mixture x.491 g pro g mixture g pro. 55 g mixture x g pro g mixture g but.

30 438 CHAPTER In mol of gas mixture, there are mol O, mol N, and mol He. Calculate the masses of these components first g O mol O x 1 mol O 8.01 g N mol N x 1 mol N 1.15 g O 1.57 g N mol He x g He 1 mol He g He The mass of mol of the gas mixture is the sum of the masses of the components: 1.15 g O g N g He 6.35 g mixture For a sample with a mass of 7.84 g, 1.15 g O 7.84 g mixture x 6.35 g mixture g O 1.57 g N 7.84 g mixture x 6.35 g mixture g N 7.84 g mixture x g He 6.35 g mixture g He 1.87 P ED P ED (X ED ) 173 mmhg (0.5) 43.5 mmhg P PD P PD (E PD ) 17 mmhg (0.75) 95.5 mmhg P P ED + P PD mmhg 1.88 P B P B (X B ) 75 mmhg (0.30).5 mmhg P T P T (E T ) mmhg (0.70) 15.4 mmhg P P B + P T mmhg

31 SOLUTIONS Calculate the moles of KAl(SO 4 ) 1H O using its molar mass of g/mol, and use this to calculate the three concentrations. a. The moles of KAl(SO 4 ) 1H O are calculated below, using the abbreviation of Hyd for the formula of KAl(SO 4 ) 1H O. mol Hyd g Hyd. x 1 mol Hyd g Hyd mol Note that one mol of KAl(SO 4 ) 1H O contains one mole of KAl(SO 4 ), so calculating the molarity of KAl(SO 4 ) can be performed using the moles of KAl(SO 4 ) 1H O. mol L mol Hyd L soln. 1 mol KAl(SO x 4) 1 mol Hyd M KAl(SO 4 ) b. The molarity of the SO 4 - ion will be twice that of the KAl(SO 4 ). - mol SO 4 L M KAl(SO 4 ) x - mol SO4 1 mol KAl(SO 4) M c. Since the density of the solution is 1.00 g/ml, the mass of L of solution is 1000 g, or kg. Since molality is moles per kg of solvent, the molality of KAl(SO 4 ) equals moles divided by kg or m (the same as the molarity) Calculate the moles of Al (SO 4 ) 3 18H O using its molar mass of g/mol, and use this to calculate the three concentrations. a. The moles of Al (SO 4 ) 3 18H O are calculated below, using the abbreviation Hyd for the formula of Al (SO 4 ) 3 18H O. mol Hyd g Hyd x 1 mol Hyd g Hyd.390 x 10-4 mol Note that one mole of Al (SO 4 ) 3 18H O contains one mole of Al (SO 4 ) 3, so calculating the molarity of Al (SO 4 ) 3 can be performed using the moles of Al (SO 4 ) 3 18H O. Molarity mol Hyd L soln x 10 mol L soln.390 x x 10-4 M (continued)

32 440 CHAPTER 1 b. The molarity of the SO 4 - ion will be three times that of the Al (SO 4 ) 3 :.390 x 10-4 mol Al (SO 4 ) 3 x - 3 mol SO4 1 mol Al (SO 4) x x 10-4 M c. Since the density of the solution is 1.00 g/ml, the mass of L of the solution is g. Of this, g is solute, so the mass of water in the solution is g kg H O The molality of Al (SO 4 ) 3 can now be calculated. Molality mol Al (SO 4) 3 kg HO x 10 mol kg.3906 x x 10-4 M 1.91 In 1.00 kg of a saturated solution of urea, there are 0.41 kg of urea (a molecular solute) and 0.59 kg of water. First, convert the mass of urea to moles x 10 3 g urea x 1 mol urea g urea 6.86 mol urea Then, find the molality of the urea in the solution: Molality mol urea kg HO 6.86 mol urea x 0.59 kg m T f K f c m (1.858 C/m)(11.57 m) 1.4 C T f 0.0 C C C 1.9 In 1.00 kg of a saturated solution of CaCl, there are 0.3 kg of CaCl (ionic) and 0.68 kg of water. First, convert the mass of CaCl to moles. 0.3 x mol CaCl g CaCl x g CaCl.88 mol CaCl (continued)

33 SOLUTIONS 441 Then, find the molality of the CaCl in the solution: mol CaCl Molality kg H O x.88 mol CaCl 0.68 kg 4.4 m For ionic solutions, T f ik f c m Calcium chloride dissolves to give three ions; thus i 3, and T f (1.858 C/m)(3)(4.4 m) 3.6 C T f 0.0 C C -4 C π 1.93 M RT 7.7 atm (0.081L atm/k mol)( )K mol/l π 1.94 M RT 5.50 atm (0.081 L atm/k mol)(5 + 73)K mol/l 1.95 Consider the equation T f ik f c m. For CaCl, i 3; for glucose i 1. Because c m 0.10 for both solutions, the product of i and c m will be larger for CaCl, as will T f. The solution of CaCl will thus have the lower freezing point Consider the equation T b ik b c m. For CaCl, i 3; for KCl it is. The product of i and c m will be larger for CaCl, as will T b. The solution of KCl will thus have the lower boiling point Assume there is L of the solution, which will contain eighteen mol H SO 4, molar mass g/mol. The mass of the solution is Mass solution 18 mol x g / mol g Thus, the density of the solution is d 180 g 1000 ml g / ml (continued)

34 44 CHAPTER 1 The mass of water in the solution is mass H O 180 g x g kg Thus, the molality of the solution is 18 mol H m SO Kg x 10 m 1.98 Assume there is L of the solution, which will contain fifteen mol H 3 PO 4, molar mass g/mol. The mass of the solution is Mass solution 15 m ol x g/mo l 179 g 0.85 Thus, the density of the solution is d 179 g 1000 ml g/ml The mass of water in the solution is mass H O 179 g x g 0.59 kg Thus, the molality of the solution is m 15 mol H3PO Kg m 1.99 Use the freezing point depression equation to find the molality of the solution. The freezing point of pure cyclohexane is 6.55 C, and K f 0. C/m. Thus m Tf Kf ( ) C 0. C/m m The moles of the compound are mol compound mol 1 kg solvent x kg 3.38 x 10-4 mol (continued)

35 SOLUTIONS 443 The molar mass of the compound is molar mass 0.15 g x 10 mol g/mol The moles of the elements in 100 g of the compound are mol Mn 8.17 g Mn x 1 mol g Mn mol mol C g C x 1 mol 1.01 g C.5645 mol mol O g O x 1 mol g O.5644 mol This gives mole ratios of one mol Mn to five mol C to five mol O. Therefore, the empirical formula of the compound is MnC 5 O 5. The weight of this formula unit is approximately 195 amu. Since the molar mass of the compound is 370. g/mol, the value of n is n 370 g / mol 195 g / unit.00, or Therefore, the formula of the compound is Mn C 10 O Use the freezing point depression equation to find the molality of the solution. The freezing point of pure cyclohexane is 6.55 C, and K f 0. C/m. Thus m Tf Kf ( ) C 0. C/m m The moles of the compound are mol compound mol 1 kg solvent x kg x 10-4 mol The molar mass of the compound is molar mass g x 10 mol g / mol (continued)

36 444 CHAPTER 1 The moles of the elements in 100 g of the compound are mol Co g Co x 1 mol g Co mol mol C 8.10 g C x 1 mol 1.01 g C.3397 mol mol O g O x 1 mol g O.3394 mol This gives mole ratios of one mol Co to four mol C to four mol O. Therefore, the empirical formula of the compound is CoC 4 O 4. The weight of this formula unit is approximately 171 amu. Since the molar mass of the compound is 335. g/mol, the value of n is n 335 g / mol 171g / unit 1.96, or Therefore, the formula of the compound is Co C 8 O a. Use the freezing point depression equation to find the molality of the solution. The freezing point of pure water is 0 C and K f C/m. Thus m Tf Kf [0 - (-.)] C C/m m The moles of the compound are mol compound mol 1 kg solvent x kg mol The molar mass of the compound is molar mass 18.0 g mol 15.0 g/mol (continued)

37 SOLUTIONS 445 The moles of the elements in 100 g of the compound are mol C g C x 1 mol 1.01 g C mol mol H 8.16 g H x 1 mol g H mol mol O 43.0 g O x 1 mol g O.7000 mol This gives mole ratios of 1.5 mol C to three mol H to one mol O. Multiplying by two gives ratios of three mol C to six mol H to two mol O. Therefore, the empirical formula of the compound is C 3 H 6 O. The weight of this formula unit is approximately 74 amu. Since the molar mass of the compound is g/mol, the value of n is n 15.0 g / mol 74 g / unit.05, or Therefore, the formula of the compound is C 6 H 1 O 4. b. The molar mass of the compound is (to the nearest tenth of a gram): 6(1.01) + 1(1.008) + 4(16.00) g/mol 1.10 a. Use the freezing point depression equation to find the molality of the solution. The freezing point of naphthalene is 80.0 C and K f 6.8 C/m. Thus m Tf Kf ( ) C 6.8 C/m 0.94 m The moles of the compound are mol compound 0.94 mol 1 kg solvent x kg.1 x 10-3 mol The molar mass of the compound is molar mass g -3.1 x 10 mol 387 g/mol (continued)

38 446 CHAPTER 1 The moles of the elements in 100 g of the compound are mol C g C x 1 mol 1.01 g C mol mol H.1 g H x 1 mol g H.19 mol mol Cl g Cl x 1 mol g C l mol This gives mole ratios of two mol C to 1.33 mol H to one mol Cl. Multiplying by three gives ratios of six mol C to four mol H to three mol Cl. Therefore, the empirical formula of the compound is C 6 H 4 Cl 3. The weight of this formula unit is approximately 18.5 amu. Since the molar mass of the compound is 387. g/mol, the value of n is n 387 g / mol 18.5 g / unit.1, or Therefore, the formula of the compound is C 1 H 8 Cl 6. b. The molar mass of the compound is (to the nearest tenth of a gram): 1(1.01) + 8(1.008) + 6(35.45) g/mol Use the freezing point depression equation to find the molality of the solution. The freezing point of pure water is 0 C, and K f 1.86 C/m. Thus m Tf Kf [0 - (-.3)] C 1.86 C/m 1.4 m Since this is a relatively dilute solution, we can assume the molarity and molality of the fish blood are approximately equal. The calculated molarity is for the total number of particles, assuming they behave ideally. π MRT 1.4 mol/l x L atm/k mol x 98. K atm